Realification of stably trivial vector bundles

The set of stably trivial complex vector bundles over complex projective space has a natural group structure whenever the corank is small. With respect to this group structure, the operations of taking the underlying real vector bundle (realification) and of adding a trivial line bundle (stablisation), are group homomorphisms.
In this talk I will explain joint work with Guy Boyde in which we build on recent enumerations by Hu of stably trivial complex bundles, to compute these homomorphisms by converting the problem into a statement in Weiss calculus, which may be computed directly.